Mathematical modeling involves the use of mathematical equations and relationships to represent biological phenomena. Complementary to this type of modeling is the use of computer simulations to represent these modeling approaches in multiple dimensions. These approaches serve two purposes. First, they provide a basic framework for the interrogation and integration of data, often providing insight into the type and quality needed for addressing a hypothesis or experimental design. This feature is especially useful when trying to integrate or analyze the large datasets generally associated with systems biology. Second, and more importantly, these models or simulations should allow one to predict the biological state under investigation and predict how the natural process will behave in various circumstances. These problems center on the understanding of the behavior of biological systems whose function is governed by the spatial and temporal ordering of multiple interacting components at the molecular, cellular, and tissue levels. We will also develop bioinformatics and bioimaging models to integrate and analyze the data generated from Component 1, and make use of the information obtained from data analysis, biological knowledge to build in silico models to model TIC behavior, cancer cell apoptosis, cell migration, cell cycle changes and drug treatment response. The goal of this component is to take advantage of our combined expertise in cell biology and computational modeling to develop coherent experimental protocols and construct biomathematical models for understanding the mechanism underiying breast cancer stem cell evolution, i.e., how one stem cell evolves into breast tumor with various sizes and compositions in cell microenvironment. Our hypothesis is that that TIC behavior during tumor development can be simulated using a robust, multiscale mathematical/computational model of TIC behavior during breast cancer development. Further, that these models can be built to reflect not only the molecular, cellular, and tissue-level dynamics, but also to allow prediction of the response of TIC to experimental therapeutics.